board the steamer Search, under my immediate direction. At the date of that report considerable progress had been made in the sounding of Saginaw bay, above the Charity islands. This work was completed by the close of the month of September, at which time, in addition to the amount of work reported (in Appendix No. 1 Annual Report,) there had been executed 360 miles of lines sounded and 210 sextant angles observed. To illustrate more fully the character of the season's operations, I herewith enclose a sketch of Saginaw bay, on a scale of 10000, on which the off-shore hydrography of the whole season is shown by the sheet marked v000, amounting to 450 square miles in all.

This hydrography has been executed with a minuteness of detail that will enable us to show the exact character of the bottom of this large estuary.

Main Triangulation.

Second Lieutenant Poe, in charge of this duty, was assiduously occupied therein till the 28th day of October, by which time he was able to accomplish the work proposed to be executed this season, to wit the triangulation of that portion of Saginaw bay above the Charity islands.

In addition to the amount of work reported by that officer, to include the 15th September, he now reports:

17 stations occupied.

1,281 pointings of the telescope.

410 readings.

170 angles measured.

The full lines on the accompanying sketch show the lines from the occupied stations, and the broken lines represent the work yet to be executed below the Charity islands, to complete the data for the chart of Saginaw bay.

Measurement of the Base Line.

At the date of the annual report the ground on which it was proposed to measure the base was being prepared by grading and otherwise for this operation.

By the 9th of October, the ground being prepared, the measurement was commenced by the party under my immediate charge, assisted by the party under the charge of Lieutenant Turnbull, topographical engineers, who had by that date completed his astronomical observations.

It is not deemed necessary to give here a description of the very ingenious and elegant apparatus belonging to the survey used on this occasion, as the same has been accurately described by Captain T. J. Lee, topographical engineers, in his report on the measurement of the Mackinac base, published in the annual report of the bureau of topographical engineers for 1854.-(See House Ex. Doc. for 1854.)

Captain Lee, in that report, states that, on testing the apparatus in the field before measuring the line, a slight want of compensation was detected in one of the measuring tubes. As the value of the apparatus was directly dependent on accuracy in this particular, I obtained the authority of the bureau, and sent for the maker, Mr. Wm. Würdemann, of Washington city, to test, and, if necessary, correct any error detected.

Mr. Würdemann, as stated in the annual report, was employed at Sand Point, in June, in making the necessary comparisons, which resulted in confirming the report of Captain Lee, and required a readjustment of the lengths of the arms of the compensating lever in tube No. 2, the one found out of order. Mr. Würdemann then communicated a singular circumstance, which I deem worthy of here recording. He stated that when he constructed the apparatus for the coast survey, at the suggestion and under the direction of Professor A. D. Bache, he adopted for the determination of the lengths of the arms of his compensating lever the ratio of the relative expansion of brass and iron, as given by the authorities of most weight, but found on testing his apparatus that it did not properly compensate. He then instituted a series of numerous experiments, and deduced from them the required ratio, which proved in the result to be correct.

When, however, he constructed the apparatus for the lake survey, he found the ratio he had previously deduced would not answer-a difference which he attributed to the fact that the brass bars of the lake survey apparatus had been in their manufacture drawn like wire, and not hammered; he therefore determined for tube No. 1 the actual expansion of the bar to be used, as he had previously done for the coast survey apparatus. As, however, the brass bars for the lake survey apparatus had been all made of the same material, in the same manner, and at the same time, and as he was somewhat pressed for time in making our apparatus, he considered he was justified in taking for tube No. 2 the ratio he had actually determined for tube No. 1. The failure of tube No. 2 to be perfectly self-compensating, proved that it was necessary to determine the actual ratio for each bar that was to be used, and that brass bars made of the same material and under identically similar circumstances, with equal dimensions, had different linear expansion for changes of temperature.

As previously stated, Mr. Würdemann adjusted the lever of compensation of tube No. 2 by successive experiments, until it was found to be perfectly self-compensating. At the same time he cleaned and adjusted both tubes and all parts of the apparatus.

The first operation in the measurement was to obtain the exact length of the tubes, by making repeated comparisons between each tube and the standard bar belonging to the apparatus, the length of which, at 620 Fahrenheit, had been established at Washington. Having carefully made these comparisons, the apparatus was transported to the west end of the line, and the measurement commenced on the 10th of October.

From this date it was continued till the 28th of October, with an intermission of three and a half days, from weather and necessary absence on my part, attending to the general duties of the survey.

In the measurement I took charge of the sector end of the tube, being relieved at times by Lieutenant Turnbull. Lieutenant Turnbull had charge of the other end of the tube, overseeing the setting of the foot plates.

The transit to regulate the alignment was placed under the charge of Assistant J. A. Potter, occasionally relieved by Assistant J. Carr, and, during the latter part of the measurement, (Assistant Potter being detached,) was entirely under Assistant Carr. The record was

kept by Assistant Wm. Casgrain. It is due to all these gentlemen to state that the service was performed in the most satisfactory manner, and to each and all my thanks are due for the commendable zeal and energy displayed by them.

It has been previously reported that triangulation stations had been erected at the termini of the proposed base. The measurement accordingly began 100 yards to the east of the western terminus. This point was marked by a limestone post sunk to the depth of three feet, and rising some six inches above the ground. The top of this post, 10 inches square, has cut in it two lines at right angles, one of which is in the general direction of the base, and the intersection is the point of beginning. To further identify this point, two reference stone posts were sunk level with the ground and at right angles to the measured line, the northern one being distant 70,75 feet, and the southern one 73% feet. These posts have on them lines cut, the intersection of which are the points of the perpendicular to the base at the distances above mentioned.

From the point of beginning an offset was measured to the northwest, at an angle of 60°, and 22 tubes measured, being about the distance of the point of beginning from the station at end of base.

The termination of this offset was marked likewise by a stone. It will be as well to remark here that the eastern end of the measured line was marked in a similar manner. The reference stones there being distant, the northern one 37.55 feet, and the southern 25.45 feet, the termination of this offset of 24 tubes was also marked by setting a stone in the ground, the offset here being to the southeast. Careful measurements, with numerous repetitions, were made of the angles of the two triangles connecting these offsets with the trigonometrical stations at each end of the base proper. In addition to the stones above described as left in the ground, there were two intermediate stones left on the measured line at the distances, respectively, of 330 and 693 tubes from point of beginning. All these stones were carefully placed in position by transferring the agate point of the tube to the stone by means of the transit on the line, and a theodolite placed at right angles, according to the method described by Captain Lee in the report above referred to.

The measurement was continued from the 10th to the 27th of October, with the intermission above mentioned of three and a half days. It has already been stated that the line passed over a series of gentle rolling sand-hills or dunes, formed by the action of the wind and sea in former times, and covered with a growth of pine and hard wood; that the line had been opened for a space of 40 feet, and ali roots removed for a space of 20 feet and graded, after being ploughed for a space of 8 feet. No better ground could be found for the use of the measuring tubes, as the sand afforded a most solid and firm bed for the foot plates, and rendering the tubes proportionately stable. Great facility in the measurement was in consequence attained, and, had it been begun with the possession of the experience acquired during its progress, the time occupied would have been very much shorter.

The following table will show the degree of progress and the amount of work each day:

It will be seen from the above that the greatest number of tubes measured in one day was 141, or a distance of four-tenths of a mile; that an average day of nine hours would give an average progress of 117 tubes, (1,755 feet,) one-third of a mile; that, of the whole number of tubes, 1,460, a little over one-third, or 509, were inclined; of these the maximum grade was 3° 48′ 10′′, and the average grade about 29'; that the average length of time occupied in measuring a single tube was, on the first day, 12 minutes 22 seconds; and on the last day, 3 minutes and 40 seconds; and for the whole measurement, 4 minutes and 38 seconds. This difference between the commencement and termination was due to the experience acquired as the measurement progressed in the manipulation and adjustments of the tubes. The average thermometer in the tube was 51°.12 Fahr., the maximum mean for a day being 71°.75, the minimum 35°.66.

In order to test the measurement, the last day's work of 40 tubes, together with one of the offsets, were remeasured, and, to enable the making of a direct comparison, the same grades with each tube were preserved. I am gratified to be able to report that no appreciable difference was perceptible in the points on the stone on transferring the agate of the tube at the end of the measurement.

The measurement terminated on the 27th of October, and on the 28th the final comparisons of the tubes with the standard bar were made, to determine their lengths. The reductions for these have been made, and a slight change observed from the same quantities as given on the 9th October before the measurement.

The adjustment of the index of the sector level was carefully examined and tested, by means of a spirit level, both before, during, and after the measurement, without detecting any index error. The reductions for the inclined tubes will, therefore, in all cases, be subtractive. These reductions are now being carefully made by two computers, which, when completed, will enable the correct length of the base to be immediately obtained.

A series of daily observations with the barometer for a period of four months at the observatory at Sand Point will afford the data for obtaining the approximate elevation of the base above the sea level and its reduction thereto.

Astronomical and magnetic observations.

Lieut. C. N. Turnbull, in charge of this department, reports that subsequently to the 15th September seven transits of the moon and